Theories of Mathematical Learning

By Leslie P. Steffe; Pearla Nesher et al. | Go to book overview

11
Theories of Mathematics Education: The Role of Cognitive Analyses

Brian Greer Queen's University, Belfast


THE COGNITIVE REVOLUTION AND BEYOND

Throughout this century, there has been a sporadic relationship between theoretical schools in psychology and the emerging field of mathematics education. In the course of this relationship, there has often been tension arising from divergent conceptions of the nature of mathematics and of the aims of mathematics education. To differing degrees, and with honorable exceptions, the psychologists who have worked on mathematics have been open to the charges of viewing mathematics selectively as a convenient domain to supply grist for their theoretical mills, and of having insufficient regard for the implementation of their theories within effective instructional environments.

Progressive exposure of the limitations of behaviorism (dominant as a theoretical school in the United States but much less so elsewhere) culminated in a sequence of events and publications during the second half of the 1950s that Gardner ( 1985) dubbed the "Cognitive Revolution." From the point of view of those involved in mathematics education, this paradigm shift had many positive aspects. The complexity of tasks used in problem-solving research increased, means for dealing with complex knowledge structures were devised, and links between the psychology of learning and school instruction were restored. Moreover, as time went on, there was a swing away from general theories of knowledge processing toward an emphasis on the domain specificity of the knowledge being processed.

During the 1960s and 1970s it looked as if cognitive psychology was in a relatively stable state with a unifying framework provided by the general concept of information processing, represented by a group of approaches bearing a family

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